How to properly model the Volute on a Capital of an Ancient Greek Column?
Concerning the main part to do it quickly... 

The idea is to notice we have a kind of spiral which is more or less the equivalent of outer and inner circles.

We know too that a subsurface modifier can do a circle from square/straight lines.

That's what we use here :

Simply follow the reference image with the fewest vertices has possible.

To do that, preset a subsurface modifier in order to view step by step the rendered curve as you add vertices.

Here I have chosen to have 5 points for half of a circle with a subdivision surface set to two:



To obtain the image above, begin to add just the contour lines. Then use the F2 addon to fill the faces (it is really quick! https://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Modeling/F2).
The important point is to have the same amount of vertices for the inner and outer part (so that they correspond and you can make faces all around).

A trick: don't close totally the face on the right of the inner circle (that will be easier for the loop cuts later).

Now... we just have a flat surface, but nearly all is composed of quads and edge loops.

From that, "loop cut and slide" with CtrlR at the center.



Then validate and move down Z this line:



Now enforce the flat parts, either adding another loop cut or beveling:



Complete filing the hole we let before, extruding the outer part and eventually add another subdivision level the the subsurface modifier.





Note: for the thinner details, as said in the comments, use normal maps or others... or spend more time to model it...